None of my website images are loaded, although paths are correct. In my Apache logs, I have plenty of :
(13)Permission denied: [client 87.231.108.18:57108] AH00
I finally found it! Thanks a ton Justin lurman to poiting out the .htaccess file. It made me see that Wordpress didn't have the right to edit my .htaccess file anymore. That was even more weird because I was 100% sure that permissions were good (even way too permissive if you ask me).
So I looked into SElinux, as I know it can play tricks on me at times and I was right. Issuing the following command solved it :
chcon -R --type=httpd_sys_rw_content_t wp-content/
I hope that helps someone else :)